Method of tuning resonance wavelength of ring resonator

ABSTRACT

Provided is a method of tuning a resonance wavelength of a ring resonator. The method of tuning the resonance wavelength of a ring resonator includes preparing a ring resonator which contains a ring waveguide and a dielectric layer covering the ring waveguide, and heating the ring resonator to induce a refractive index phase change of the dielectric layer.

CROSS-REFERENCE TO RELATED APPLICATIONS

This U.S. non-provisional patent application claims priority under 35U.S.C. §119 of Korean Patent Applications No. 10-2010-0095996, filed onOct. 1, 2010, the entire contents of which are hereby incorporated byreference.

BACKGROUND

The present disclosure herein relates to an optical communicationdevice, and more particularly, to a method of tuning a resonancewavelength of a ring resonator.

According to the miniaturization and high-speed trends of electronicdevices, researches are continuing in order to increase the integrationdensity of components which constitute the electronic devices. For theminiaturization and high-speed operation of the electronic devices, arapid signal transmission between the components is required togetherwith the miniaturization of the components.

As a way of rapid signal transmission between the components, anapplication of optical communication technologies to electronic devicesis being attempted. In the case where the optical communicationtechnologies are applied to the electronic devices, the signaltransmission can be performed at higher speed and the disadvantages of arelated art signal transmission method such as high resistance,high-heat generation and parasitic capacitance phenomenon, etc., can bemitigated.

The essential optical devices for applying the optical communicationtechnologies to a silicon-based semiconductor chip may include asilicon-based optical switch, an optical modulator, a multiplexer(MUX)/demultiplexer (DEMUX) filter and the like, in addition to a lightsource and an optical detector. Although the roles and functions of theoptical switch, the optical modulator and the MUX/DEMUX filter amongthese are different, there are many cases where the core manufacturingtechnologies are shared or the same device is applied differently. Forexample, in the case of a ring resonator, it can be applied to all ofthe above three devices such that active researches are in progress.

Particularly, in order to achieve a multi-core central processing unit(CPU) which is one of the goals of silicon photonics research, a commonopinion of scholars is that the following key difficult problems of aring resonator should be solved. First, the statistical errors ofresonance wavelength, which essentially occurs during the manufacturingprocess of the ring resonator, should be minimized. Second, a tuningmethod should exist to match the resonance wavelengths, when theresonance wavelengths between more than two ring resonators should bematched to each other in the semiconductor chip with a plurality of ringresonators. Third, a photolithography process is able to manufacture theminimum gap between a ring waveguide and a bus line or a ring waveguideand a ring waveguide.

SUMMARY

The present disclosure provides a method of tuning a resonancewavelength of a ring resonator with improved operating characteristics.

Embodiments of the inventive concept provide a method of tuning aresonance wavelength of a ring resonator, the method including:preparing a ring resonator containing a ring waveguide and a dielectriclayer covering the ring waveguide; and heating the ring resonator toinduce a refractive index phase change of the dielectric layer.

In some embodiments, a temperature of the refractive index phase changeis determined by a deposition temperature of the dielectric layer.

In other embodiments, the ring waveguide includes silicon, and thedielectric layer at least may include a cladding dielectric layercovering upper and lower surfaces of the ring waveguide, and a firstsubsidiary dielectric layer covering an upper surface of the ringwaveguide and disposed between the cladding dielectric layer and thering waveguide.

In still other embodiments, the cladding dielectric layer includes asilicon oxide layer, and the first subsidiary dielectric layer mayinclude a silicon oxynitride layer (SiO_(x)N_(y)).

In even other embodiments, the first subsidiary dielectric layer maycover upper and side surfaces of the ring waveguide.

In yet other embodiments, the dielectric layer may further include asecond subsidiary dielectric layer covering the upper surface of thering waveguide and disposed between the first subsidiary dielectriclayer and the ring waveguide, wherein the second subsidiary dielectriclayer may include a silicon nitride layer.

In further embodiments, the ring waveguide includes a plurality of ringwaveguides, and any one of the plurality of ring waveguides is heated tochange a resonance wavelength, and a temperature and a resonancewavelength of another one of the plurality of ring waveguides aremaintained constantly.

In still further embodiments, the ring waveguide allows light of a TMmode to move.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the inventive concept, and are incorporated in andconstitute a part of this specification. The drawings illustrateexemplary embodiments of the inventive concept and, together with thedescription, serve to explain principles of the inventive concept. Inthe drawings:

FIGS. 1A and 1B are drawings of 3^(rd) order and 1^(st) order ringresonators conceptually illustrating a multi-channel filter or anadd-drop switch;

FIGS. 2A and 2B are graphs showing spectrum characteristics of 3^(rd)order and 1^(st) order ring resonators;

FIG. 3A is a drawing illustrating specific design values for a 3^(rd)order ring, and FIG. 3B is a scanning electron microscope (SEM)micrograph taken along line I-I′ of FIG. 3A;

FIGS. 4A and 4B are graphs showing 16-channel and 32-channeltransmission spectrums when a 3^(rd) order ring resonator is used as afilter;

FIG. 5A is a flowchart illustrating a method of tuning a resonancewavelength of a ring resonator according to an embodiment of theinventive concept;

FIGS. 5B and 5C are cross-sectional views illustrating ring resonatorsaccording to embodiments of the inventive concept; and

FIG. 6A is a graph showing a change of resonance wavelength depending ona temperature of a ring resonator according to an embodiment of theinventive concept, and FIG. 6B is a graph showing the change ofresonance wavelength with respect to a heating time at a specifictemperature.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The above objects, other objects, features and advantages of the presentinvention will be better understood from the following description ofpreferred embodiments taken in conjunction with the accompanyingdrawings. The present invention may, however, be embodied in differentforms and should not be construed as limited to the embodiments setforth herein. Rather, these embodiments are provided so that thisdisclosure will be thorough and complete, and will fully convey thescope of the present invention to those skilled in the art.

In the specification, it will be understood that when one element isreferred to as being ‘on’ another element, it can be directly on theother element, or intervening elements may also be present. In thefigures, moreover, the dimensions of elements are exaggerated forclarity of illustration. Like reference numerals refer to like elementsthroughout.

The embodiments in the detailed description will be described withsectional views and/or plan views as ideal exemplary views of theinventive concept. In the drawings, the dimensions of layers and regionsare exaggerated for clarity of illustration. Areas exemplified in thedrawings have general properties, and are used to illustrate a specificshape of a device region. Thus, this should not be construed as limitedto the scope of the inventive concept. It will be understood thatalthough the terms first, second and third are used herein to describevarious elements, these elements should not be limited by these terms.These terms are only used to distinguish one element from anotherelement. An embodiment described and exemplified herein includes acomplementary embodiment thereof.

While specific terms were used in the specification, they were not usedto limit the inventive concept, but merely used to explain the exemplaryembodiments. In the inventive concept, the terms of a singular form mayinclude plural forms unless otherwise specified. The meaning of“include,” “comprise,” “including,” or “comprising,” specifies aproperty, a region, a fixed number, a step, a process, an element and/ora component but does not exclude other properties, regions, fixednumbers, steps, processes, elements and/or components.

Two important phenomena are first discovered from researches andexperiments performed by the present inventors. It is considered thatthese will be an important key to solve three difficult problems of aring resonator described above.

The first phenomenon may reduce the statistical errors of resonancewavelength by more than two times in the case of using the lowest orderof a transverse magnetic (TM) mode. Also, the minimum gap between thering waveguide and the bus line or the ring waveguide and the ringwaveguide may be made more than about 400 nm such that the ringresonator can be manufactured by the photolithography process.

The second phenomenon is that a refractive index phase change phenomenonis observed in the case where a temperature of a silicon oxynitride(SiO_(x)N_(y)) layer, which was deposited by a plasma enhanced chemicalvapor deposition (PECVD) equipment at a specific temperature, isincreased by further heating. Herein, the refractive index phase changephenomenon denotes a phenomenon in which the change of refractive indexis almost absent or very small below a deposition temperature, but, incontrast, the refractive index increases very much above the depositiontemperature. This means that the resonance wavelength of the ringresonator may be easily and precisely changed when inserting the siliconoxynitride layer to an upper cladding layer of a waveguide.

Based on this research, a method of tuning a resonance wavelength of aring resonator according to the embodiments of the inventive conceptwill be described below.

FIGS. 1A and 1B are drawings of 3^(rd) order and 1^(st) order ringresonators conceptually illustrating a multi-channel filter or anadd-drop switch.

Referring to FIGS. 1A and 1B, when signals of a plurality of channelsare inputted to an input port, if a wavelength of channel 1 (λ₁) matcheswith a resonance wavelength of a ring resonator, and a wavelengths ofchannels 2 and 3 (λ₂ and λ₃) do not match with the resonance wavelength,a signal of channel 1 is outputted from a drop port via ring(s) andsignals of channels 2 and 3 are transmitted to a through port. Thisconfiguration allows the ring resonator to function as a demultiplexer(DEMUX). Also, on the contrary, when the λ₁ signal is inputted to an addport and the λ₂ and λ₃ signals are inputted to the through port, thisconfiguration allows the ring resonator to function as a multiplexer(MUX) by which λ₁, λ₂ and λ₃ are outputted from the input port. If theresonance wavelength of one among three rings is changed, the signal ofchannel 1 may be changed from the add port to the through port or fromthe input port to the drop port. This means that the ring resonator mayfunction as an add-drop switch. In addition, when the resonancewavelength of one among three rings is modulated over time, the ringresonator may function as a modulator and the experiments prove that amodulation rate is more than about 10 GHz.

FIGS. 2A and 2B are graphs showing spectrum characteristics of 3^(rd)order and 1^(st) order ring resonators.

Referring to FIGS. 2A and 2B, a 1^(st) order ring resonator may have thesame function as a 3^(rd) order ring resonator. However, spectrumcharacteristics of the 3^(rd) order ring resonator are far superior. Themost important characteristics of a filter, a cross talk with adjacentchannels and a flat-top spectral shape, will be superior as the order ofa ring resonator is higher. However, since resonance wavelengths of theserially connected rings should match exactly with each other, a processwill be extremely difficult as the order of the ring resonator ishigher. In particular, a mismatch of resonance wavelength showsstatistical characteristics such that it is impossible to matchcompletely.

FIG. 3A is a drawing illustrating specific design values for a 3^(rd)order ring, and FIG. 3B is a scanning electron microscope (SEM)micrograph taken along line I-I′ of FIG. 3A.

Referring to FIGS. 3A and 3B, a 3^(rd) order ring resonator 100 includesa first port 110, a second port 120 and three ring waveguides 150arranged between the first port 110 and the second port 120. Asdescribed in FIG. 1A, the first port 110 may include an input port and athrough port, and the second port 120 may include a drop port and an addport.

The width W and height H of each of the ring waveguides 150 are about 1mm and about 190 nm, respectively, and a gap G1 of a coupling region isabout 400 nm and a gap G2 between the ring waveguides 150 is about 600nm, and a radius of the ring waveguide 150 is about 9 mm. A lightpassing through the ring waveguide 150 uses a transverse magnetic (TM)mode. The ring waveguide 150 may be formed using the Hg I-linephotolithography process. The values described herein are experimentallyoptimized values for obtaining a good transmission spectrum. However, arelatively good transmission spectrum may also be obtained from thevalues which considerably deviate from these values. For example, a goodtransmission spectrum may be obtained by appropriate combinations of theranges in which the width W of the ring waveguide 150 is about 0.5-1.5μm, the height H of the ring waveguide 150 is about 100-350 nm, and thegap G1 between the ring waveguides 150 and the first and second ports110 and 120, and the gap G2 between the ring waveguides 150 are about200 nm-1 mm. Also, the radius R of the ring waveguide 150 may be morethan 5 μm.

FIGS. 4A and 4B are graphs showing 16-channel and 32-channeltransmission spectrums when a 3^(rd) order ring resonator is used as afilter.

Referring to FIGS. 4A and 4B, it can be understood that a 3^(rd) orderring resonator with the experimentally optimized values in FIGS. 3A and3B exhibits considerably superior filter characteristics with respect to16-channel and 32-channel.

The excellent spectrum characteristics presented in FIGS. 4A and 4B areonly possible if an optical waveguide is designed such that a lightmoves only in the lowest order of a TM mode. In most of the ringresonators which have been reported in the articles so far, theiroptical waveguides are designed to have the lowest order of a transverseelectric (TE) mode. In the case of the TE mode, the light is morestrongly condensed at a core of the optical waveguide as compared to theTM mode so that the bending loss will be small. Therefore, there areadvantages that the ring resonator with a much smaller radius can beachieved and a thickness of a cladding layer can be made much smaller.

However, the light is strongly condensed at the core of the opticalwaveguide so that the statistical wavelength errors caused bymanufacturing processes are rather very large, and since a gap for anoptical connection between a ring and a bus line or a ring and a ringshould be small, there is a disadvantage that electron-beam lithographyshould be used. These two disadvantages are being the most difficultproblems of silicon photonics research.

From the research performed by the present inventors, it wasexperimentally found that the above disadvantages may be overcome whenthe optical waveguide and the ring resonator are properly designed byusing the TM mode. That is, the statistical wavelength errors caused bymanufacturing processes are reduced more than two times and the radiusof the ring is also about 9 mm which is an acceptable size, and ringfilters of 16-channel with 100 GHz channel spacing and 32-channel with50 GHz channel spacing are manufactured, and the excellent filterspectrums are measured as shown in FIGS. 4A and 4B. Also, the minimumgap between the ring and the bus line or the ring and the ring can bemore than about 400 nm. Therefore, a 32-channel MUX/DEMUX ring filtercan be manufactured by the Hg I-line photolithography process.Specifically, referring to FIGS. 3A and 3B, the dimensions of ringfilters of 16-channel with 100 GHz channel spacing and 32-channel with50 GHz channel spacing may be specified that the width W and height H ofthe ring waveguide 150 are about 1.0 μm and about 190-200 nm,respectively, and the gap G1 between the ring waveguides 150 and thefirst and second ports 110 and 120 is about 400-700 nm, and the radius Rof the ring waveguide 150 is about 8-10 μm.

FIG. 5A is a flowchart illustrating a method of tuning a resonancewavelength of a ring resonator according to an embodiments of theinventive concept.

Referring to FIG. 5A, in operation S1, a ring resonator, which includesa ring waveguide and a dielectric layer covering the ring waveguide, isprepared. The specific structure of the ring waveguide and thedielectric layer will be described below with reference to FIGS. 5B and5C. In operation S2, a refractive index phase change of the dielectriclayer is induced by heating the ring resonator. The heating of the ringresonator includes preliminarily heating of the ring resonator below thedeposition temperature of the dielectric layer, and heating any one of aplurality of ring waveguides to a temperature above the depositiontemperature of the dielectric layer. That is, a temperature of therefractive index phase change may be determined by the depositiontemperature of the dielectric layer. The ring waveguide includes aplurality of ring waveguides, and the refractive index phase change maybe induced by heating the specific one of the plurality of ringwaveguides.

FIG. 5B is a cross-sectional view illustrating a ring resonatoraccording to an embodiment of the inventive concept, and FIG. 5C is across-sectional view illustrating a ring resonator according to anotherembodiment of the inventive concept. FIGS. 5B and 5C are cross-sectionalviews taken along line I-I′ of FIG. 3A.

Referring to FIG. 5B, a ring resonator 300 includes a lower claddingdielectric layer 342 on a substrate 330, a ring waveguide 350 on thelower cladding dielectric layer 342, a first subsidiary dielectric layer345 covering the ring waveguide 350 and the lower cladding dielectriclayer 342, and an upper cladding dielectric layer 347 on the firstsubsidiary dielectric layer 345. The lower cladding dielectric layer342, the first subsidiary dielectric layer 345 and the upper claddingdielectric layer 347 may constitute a dielectric layer 340.

The lower cladding dielectric layer 342 and the upper claddingdielectric layer 347 may include a silicon oxide layer. The ringwaveguide 350 may include silicon. The first subsidiary dielectric layer345 may include a silicon oxynitride layer or a silicon nitride layer.

The first subsidiary dielectric layer 345 may be disposed to cover theupper and side surfaces of the ring waveguide 350. Therefore, an opticalsignal via the ring resonator 300 may be more affected by the refractiveindex phase change of the first subsidiary dielectric layer 345.

Referring to FIG. 5C, a ring resonator 400 includes a lower claddingdielectric layer 442 on a substrate 430, a ring waveguide 450 on thelower cladding dielectric layer 442, a first subsidiary dielectric layer445 covering the ring waveguide 450 and the lower cladding dielectriclayer 442, a second subsidiary dielectric layer 446 covering an uppersurface of the ring waveguide 450 and disposed between the firstsubsidiary dielectric layer 445 and the ring waveguide 450, and an uppercladding dielectric layer 447 on the first subsidiary dielectric layer445. The lower cladding dielectric layer 442, the first subsidiarydielectric layer 445, the second subsidiary dielectric layer 446 and theupper cladding dielectric layer 447 may constitute a dielectric layer440.

The lower cladding dielectric layer 442 and the upper claddingdielectric layer 447 may include a silicon oxide layer. The ringwaveguide 450 may include silicon. The first subsidiary dielectric layer445 may include a silicon oxynitride layer. The second subsidiarydielectric layer 446 may include a silicon nitride layer.

FIG. 6A is a graph showing a change of resonance wavelength depending onthe temperature of a ring resonator according to an embodiment of theinventive concept, and FIG. 6B is a graph showing the change ofresonance wavelength with respect to a heating time at a specifictemperature.

A resonance wavelength change according to a temperature of a ringresonator shown in FIG. 6A is caused by a refractive index phase changeaccording to a temperature of a silicon oxynitride layer, and this isthe first discovered phenomenon in the present researches. Therespective samples A, B and C have different heating time from eachother, wherein a heating time of sample A is longer than that of sampleB, and a heating time of sample B is longer than that of sample C. Asilicon oxynitride (SiO_(x)N_(y)) layer may have a refractive indexvalue ranging from n=1.45, a refractive index of a silicon oxide (SiO₂)layer to n=2.0, a refractive index of a silicon nitride (Si₃N₄) layerdepending on the concentration ratio of oxygen and nitrogen. In thepresent researches, the silicon oxynitride (SiO_(x)N_(y)) layer is usedfor the first subsidiary dielectric layer 345 in the waveguide structurelike FIG. 5B, and the temperature characteristics of the resonancewavelength of the ring resonator are measured. The lower cladding layer342 is a silicon oxide (SiO₂) layer of a silicon on insulator (SOI)substrate, and the first subsidiary dielectric layer 345 and the uppercladding layer 347 are a silicon oxynitride (SiO_(x)N_(y)) layer and asilicon oxide (SiO₂) layer deposited by a plasma enhanced chemical vapordeposition (PECVD) equipment at about 400° C., respectively.

The results, which are obtained by measuring the resonance wavelength ateach temperature while heating a multichannel ring resonator to about430° C. by a heater, show useful characteristics like in FIG. 6A. Theresonance wavelength change is not observed below about 300° C. and theresonance wavelength begins to move slowly to a longer wavelength atabout 300-400° C., and the resonance wavelength increases steeply to alonger wavelength at about 400° C.

As the result of performing the same experiment after replacing thesilicon oxynitride (SiO_(x)N_(y)) layer with the silicon oxide (SiO₂)layer deposited by the PECVD at about 400° C., the resonance wavelengthmovement is not observed at all. As the result of experiments, it can beunderstood that the silicon oxynitride (SiO_(x)N_(y)) layer shows arefractive index phase change phenomenon in which the refractive indexincreases rapidly at the deposition temperature. As the result ofperforming the same experiment after depositing the silicon oxynitride(SiO_(x)N_(y)) layer at about 300° C., it is also observed a phenomenonin which the refractive index of the silicon oxynitride (SiO_(x)N_(y))layer increases largely at about 300° C. But, the increasing rate ofrefractive index in the case of depositing at about 400° C. shows largervalue than that in the case of depositing at about 300° C.

FIG. 6B shows the change of resonance wavelength with respect to aheating time after holding a temperature of a heater at about 415. Itcan be understood that the increasing rate of refractive index is largeat the beginning of heating and the increasing rate of refractive indexlowers over time.

The experimental results presented in FIGS. 6A and 6B may not only bevery usefully applied to a silicon resonator, but also to all siliconwaveguides having wavelength dependency on the waveguide light. Theseindicate that the resonance wavelength can always accurately return toits original position by heating the manufactured device when thesilicon oxynitride (SiO_(x)N_(y)) layer is inserted into a claddinglayer and the resonance wavelength deviates from a fixed value to thedirection of a low refractive index value.

When trying to change only the resonance wavelength of a specific ringresonator with respect to the chip containing a plurality of ringresonators, after heating the entire chip to about 300-350, the specificring resonator is heated by laser or a tip of a heated needle and thelike, thereby enabling to change the resonance wavelength of thecorresponding ring. At this time, it can be understood that the changeof resonance wavelength may not be shown for the ring resonator in theposition farther than the distance having about 50-100° C. oftemperature slope.

According to the embodiments of the inventive concept, a resonancewavelength of a ring resonator can be changed by inducing a refractiveindex phase change phenomenon of a dielectric layer. The refractiveindex phase change phenomenon is determined by a deposition temperatureof the dielectric layer such that the resonance wavelength of the ringresonator can be effectively tuned by heating a specific ring waveguideabove the deposition temperature of the dielectric layer.

The above-disclosed subject matter is to be considered illustrative andnot restrictive, and the appended claims are intended to cover all suchmodifications, enhancements, and other embodiments, which fall withinthe true spirit and scope of the inventive concept. Thus, to the maximumextent allowed by law, the scope of the inventive concept is to bedetermined by the broadest permissible interpretation of the followingclaims and their equivalents, and shall not be restricted or limited bythe foregoing detailed description.

What is claimed is:
 1. A method of tuning a resonance wavelength of aring resonator, the method comprising: preparing the ring resonatorincluding a ring waveguide and a dielectric layer covering the ringwaveguide, the dielectric layer being deposited at a depositiontemperature; and heating the ring resonator to a first temperature, thefirst temperature being lower than the deposition temperature; andheating the ring resonator to a second temperature, the secondtemperature being higher than the first temperature to induce arefractive index phase change of the dielectric layer, wherein arefractive index of the dielectric layer remains substantially the samebelow the first temperature.
 2. The method of claim 1, wherein the ringwaveguide comprises silicon, and wherein the dielectric layer at leastcomprises upper and lower cladding dielectric layers covering upper andlower surfaces of the ring waveguide, respectively, and a firstsubsidiary dielectric layer covering an upper surface of the ringwaveguide, the first subsidiary dielectric layer being disposed betweenthe upper cladding dielectric layer and the ring waveguide.
 3. Themethod of claim 2, wherein the upper and lower cladding dielectriclayers comprise a silicon oxide layer, and the first subsidiarydielectric layer comprises a silicon oxynitride layer (SiO_(x)N_(y)). 4.The method of claim 2, wherein the first subsidiary dielectric layercovers upper and side surfaces of the ring waveguide.
 5. The method ofclaim 2, wherein the dielectric layer further comprises a secondsubsidiary dielectric layer covering the upper surface of the ringwaveguide and disposed between the first subsidiary dielectric layer andthe ring waveguide.
 6. The method of claim 1, wherein the ring waveguidecomprises a plurality of ring waveguides, and wherein any one of theplurality of ring waveguides is heated to the second temperature tochange a resonance wavelength, and a temperature and a resonancewavelength of another one of the plurality of ring waveguides aremaintained constantly.
 7. The method of claim 1, wherein the ringwaveguide allows light of a transverse magnetic (TM) mode to beswitched.
 8. The method of claim 5, wherein the second subsidiarydielectric layer comprises a silicon nitride layer.
 9. The method ofclaim 3, wherein the first subsidiary dielectric layer is depositedusing a plasma enhanced chemical vapor deposition (PECVD).
 10. Themethod of claim 9, wherein the PECVD is performed at the depositiontemperature around 400° C.
 11. The method of claim 10, wherein the firsttemperature is around 300° C.
 12. A method of tuning a resonancewavelength of a ring resonator, the method comprising: preparing thering resonator including a ring waveguide and a dielectric layercovering the ring waveguide, the dielectric layer being deposited at adeposition temperature; heating the ring resonator to a firsttemperature, the first temperature being lower than the depositiontemperature; and heating the ring waveguide of the ring resonator to asecond temperature, the second temperature being higher than the firsttemperature to induce a refractive index phase change of the dielectriclayer, wherein a refractive index of the dielectric layer remainssubstantially the same below the first temperature, wherein the ringwaveguide comprises silicon, and wherein the dielectric layer comprisesupper and lower cladding dielectric layers covering upper and lowersurfaces of the ring waveguide, respectively, and a first subsidiarydielectric layer covering an upper surface of the ring waveguide and anentire upper surface of the lower cladding dielectric layer, the firstsubsidiary dielectric layer being disposed between the upper claddingdielectric layer and the ring waveguide.